Question

A gramophone disc of brass of diameter \[30cm\] rotates horizontally at the rate of \[\dfrac{{100}}{3}\] revolutions per minute. If the vertical component of the earth’s magnetic field is\[0.01Wb{m^2}\], then calculate the EMF induced between the center and the rim of the disc.

Answer 1

Hint: It's the generation of a potential difference in a coil as a result of changes in the magnetic flux passing through it.
When the flux link with a conductor or coil shifts, electromotive Force, or EMF, is said to be induced.

Complete step-by-step solution:
The EMF induced in a circuit is directly proportional to the time rate of change of the magnetic flux through a circuit.
Induction occurs when a change in magnetic flux causes an electromotive force (EMF) to oppose the change. One of the most common causes of induction is motion. A magnet moving toward a coil, for example, generates an EMF, and a coil moving toward a magnet produces a similar EMF.
Flux passing through the disc
\[\phi = BA\]
\[\phi = B\pi {r^2}\]
\[\phi = 0.01 \times 3.14 \times {(15 \times {10^{ - 2}})^2}\]
\[ = 7.065 \times {10^{ - 4}}Wb\]
Rate of cutting flux (Induced EMF) = \[\phi \times rev/\sec \]
   \[ = 7.065 \times {10^{ - 4}} \times \dfrac{{100}}{{3 \times 60}}\]
  \[ = 3.9 \times {10^{ - 4}}Volts\]
Answer \[ = 3.9 \times {10^{ - 4}}Volts\]

Note: Michael Faraday was the first to discover electromagnetic induction in the\[1830s\]. As Faraday moved a permanent magnet in and out of a coil or a single loop of wire, he found that an Electromotive Force or EMF, or voltage, was induced, and thus a current was formed.
An EMF induced in a conductor as it travels through a magnetic field is referred to as dynamically induced EMF. When a conductor of duration travels over a \[wb/{m^2}\] as seen in the diagram. The dynamically induced EMF is induced in the conductor when the flux density is velocity.
If the coil's current is shifted, the flux connected to its own turns changes as well, resulting in self-induced e.m.f. The EMF induced in a stationary conductor due to a change in flux (the field is moving) is known as statically induced EMF and is found in transformers.